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Is massively collaborative mathematics scalable?

I’ve been watching, though not particularly intently, Tim Gowers’s attempt massively collaborative mathematics. I’m not sure if I’ve looked hard enough to judge, but it certainly looks as though it were quite successful. This of course, answers Tim’s original question “is massively collaborative mathematics possible?” positively, but I still have to wonder if it’s sustainable in the long term. Of course, it never seems smart to bet against the possibilities of the Internet combining disperate contributions into valuable knowledge. Certainly, I would say people have tended to underestimate the possibilities of real advances coming from the technology of wikis and blogs. At the same time, it seems hard to imagine that people will really have the energy and time, not to mention mental organization, to follow several such projects at all closely. One of Tim’s take away lessons from the project seemed to be that it shrank in number of participants faster than he expected. And this was in a collaboration prominently featuring two Fields medalists and promoted on what is probably the world’s most prestigious math blog! It seems more likely that as the number of such projects expands the average number of participants will shrink until most are functionally equivalent of the collaborations we are used to today, just with more efficient coauthor location. By which I mean, the important advance will not be the number of people involved, but rather the identity of them.

Not that the value of efficient coauthor location should be minimized! The broader array of people we can stay in contact with due to the Internet is a huge boon to mathematics. It’s just that I suspect any concern over how we will deal with the allocating credit in a 20 person collaboration is a bit premature, at least outside of exceptional cases.

On the other hand, I’m kind of excited about the possibility of proving myself wrong, but haven’t been able to come up with any good projects. Does anyone wanna do that massively collaboratively?

On the other hand, it’s one thing to say “here’s an interesting open problem” and quite another to come up with lines of attack on the problem that can be pursued in a massively collaborative project.

Right. I think “open problem” lists have never been very useful for me, in part because I have very little interest in thinking about problems I have no idea how to solve. There are already too many that I have some idea about to bother with those. Unfortunately, none of the ones that have popped to mind yet strike me as very good for massive collaboration.

I think one project which is desperately crying out for massive collaboration is a reorganization of mathematical pedagogy (at university level) along modern lines and, ideally, freely available.

This would be an enormous project, with small payoff in terms of prestige for those participating (although the Bourbaki program suggests that new mathematics develops when we rethink our basic definitions). The value of such a system would be significant for both students and professors (in the form of freely available lecture notes and presentation materials).

One thing worth pointing out is that, as far I understand, the most successful massively collaborative software projects involve writing code, not inventing algorithms. And while compilable code is an order of magnitude or two more formal than your average math paper, writing it is still just writing. If someone asks if you can write an operating system with properties X, Y, and Z, then answer is just Yes. The more interesting question is how long it will take. This is like writing in mathematics. Could I write a textbook on Perelman’s proof, about which I know nothing? Of course. It might take me years to learn the background necessary to even begin reading his work, but I could do it, simply because everything needed has already been explained. But now I can’t say the same for most open problems in mathematics or anything else. That’s why they’re open.

So I submit that the projects that lend themselves best to massive collaboration are those that involve a lot of work in well-understood areas and that these are typically writing projects. So writing a new operating system, writing an encyclopedia, and writing an algebraic geometry textbook all seem well-suited to massive collaboration, but solving open problems doesn’t seem so, to me.

Those are certain important and worthwhile projects, but I think we already know this model works for exposition (see Wikipedia), but I think it’s an open question whether it will really work on a large scale for research. We’ve seen shifts like this before; email was a huge leap forward for the possibilities of collaborating in mathematics, but it’s very difficult to really engage a large number of people in a single research project. There are too many projects and not enough interested people.

I think one project which is desperately crying out for massive collaboration is a reorganization of mathematical pedagogy (at university level) along modern lines and, ideally, freely available.

Along all lines, really. This brought up a vigorous debate in a math-ed blog recently. One person thought we needed grad students with a lot of time on their hands to pull it off. I just think we need to somehow go past the social “event horizon” which forms a self-sustaining community (that is, enough people that the natural churn that happens when participants have babies / work on their dissertation / etc. it doesn’t interfere with the project). There’s probably an equation to describe this.

Oh, as far as starting a new polymath goes, I still have my marbles in the other one (I want to help with the paper writeup … if previously mentioned baby would give me a breather) but if it’s combinatorics and/or computer science again I’d be happy to chip in.

I think one project which is desperately crying out for massive collaboration is a reorganization of mathematical pedagogy (at university level) along modern lines and, ideally, freely available.

Having been in discussions about the possibility of doing such a thing locally, I should point out that one of the major restrictions on such an effort on the first-year/sophomore level are the requirements of other departments for their students to learn particular bits of mathematics in their only semester or only two semesters of mathematics courses. At almost every institution it would be a disaster for a math department (as in tenured professors would have to be laid off) if the biology department decided to teach their own version of calculus.

Producing the materials and attempting to force them into calculus classes are entirely separate operations. The materials could be quite valuable, even if people rarely teach classes directly out of them.

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It’s just that I suspect any concern over how we will deal with the allocating credit in a 20 person collaboration is a bit premature, at least outside of exceptional cases.
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The main problem is trying to get people to participate in such things. Are you really so sure that credit doesn’t play a factor? Personally, I think that such a notion is rather naive.

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